Answer:
83.85% of 1-mile long roadways with potholes numbering between 22 and 58
Explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 49
Standard deviation = 9
Using the Empirical Rule, what is the approximate percentage of 1-mile long roadways with potholes numbering between 22 and 58?
22 = 49 - 3*9
So 22 is three standard deviations below the mean.
Since the normal distribution is symmetric, 50% of the measures are below the mean and 50% are above the mean.
Of those 50% which are below the mean, 99.7% of those are within 3 standard deviations of the mean, that is, greater than 22.
58 = 49 + 9
So 58 is one standard deviation of the mean.
Of those which are above the mean, 68% are within 1 standard deviation of the mean, that is, lesser than 58.
Then
0.997*0.5 + 0.68*0.5 = 0.8385 = 83.85%
83.85% of 1-mile long roadways with potholes numbering between 22 and 58